Problem: Simplify to lowest terms. $\dfrac{72}{63}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 72 and 63? $72 = 2\cdot2\cdot2\cdot3\cdot3$ $63 = 3\cdot3\cdot7$ $\mbox{GCD}(72, 63) = 3\cdot3 = 9$ $\dfrac{72}{63} = \dfrac{8 \cdot 9}{ 7\cdot 9}$ $\hphantom{\dfrac{72}{63}} = \dfrac{8}{7} \cdot \dfrac{9}{9}$ $\hphantom{\dfrac{72}{63}} = \dfrac{8}{7} \cdot 1$ $\hphantom{\dfrac{72}{63}} = \dfrac{8}{7}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{72}{63}= \dfrac{3\cdot24}{3\cdot21}= \dfrac{3\cdot 3\cdot8}{3\cdot 3\cdot7}= \dfrac{8}{7}$